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J. Korean Math. Soc. 2011; 48(5): 1083-1100

Printed September 1, 2011

https://doi.org/10.4134/JKMS.2011.48.5.1083

Copyright © The Korean Mathematical Society.

Spacelike maximal surfaces, timelike minimal surfaces, and Bj\"{o}rling representation formulae

Young Wook Kim, Sung-Eun Koh, Heayong Shin, and Seong-Deog Yang

Korea University, Konkuk University, Chung-Ang University, Korea University

Abstract

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We show that some class of spacelike maximal surfaces and timelike minimal surfaces match smoothly across the singular curve of the surfaces. Singular Bj\"{o}rling representation formulae for generalized spacelike maximal surfaces and for generalized timelike minimal surfaces play important roles in the explanation of this phenomenon.

Keywords: spacelike maximal surface, timelike minimal surface, Bj\"{o}rling representation formula

MSC numbers: 53A35, 53B30

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